\documentclass[UTF8]{ctexart}
\usepackage{amsmath}
\begin{document}
\section{方差的性质}

\[
  \exists c \text{ such that } P(X = c) = 1  \implies Var(X) = 0
\]

\begin{align*}
  P(X=c) = 1 &\implies E(X)=c\\
             &\implies P[(X-c)^2=0] = 1\\
             &\implies Var(X) = 0
\end{align*}

\[
  Var(X) = 0 \implies \exists c \text{ such that } P(X = c) = 1
\]

\begin{align*}
  \left.
    \begin{gathered}
      Var(X) = E[(X-\mu)^2] = 0\\
      P[(X-\mu)^2\ge 0] = 1
    \end{gathered}
  \right\}
  &\implies P[(X-\mu)^2=0] = 1\\
  &\implies P(X=\mu)=1
\end{align*}
\end{document}
